Questions tagged [modern-portfolio-theory]
A theoretical framework for analyzing investment portfolios based on their expected return and risk.
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Asset rate (elasticities ?) of substitution
I'm kind of a newbie in the finance research area. However, I'm working on cross-asset spillovers (transmission of shocks between assets) and my guess is that it comes from investors behaviors. ...
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Risk Aversion Coefficient Literature Rationale and Sources
I'm running a Black-Litterman model and for the Risk Aversion Coefficient I have two potential formulas.
The first is the standard formula which I believe is used in the original Black-Litterman ...
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Risk free rate must be lower than expected return of global minimum variance portfolio
I heard a professor say: "We know the return of the risk free asset must be less than the expected return of the global minimum variance portfolio, otherwise there would be arbitrage ...
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"Risk Matters Hypothesis" - does it really?
Risk.net has recently run a story about the "risk matters hypothesis" which refers to Sharpe’s Arithmetic and the Risk Matters Hypothesis by Haghani, Ragulin and White (2023).
If I ...
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Excess Return Covariance Matrix is Singular - Cash return and risk free rate are the same [closed]
I've created a three asset excess return covariance matrix. The assets are; equity, bonds, and cash. However, my cash return is the same as my risk free rate ( i.e. 3 month Euribor). This is leaving ...
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Reverse optimization: How to generate the expected portfolio returns given the weights and a series of constraints on those weights?
I have the below function in Python. My objective is to back out the expected returns associated with certain portfolio weights given a series of assumptions.
From this I want to generate the expected ...
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How to construct a delta-neutral portfolio containing stocks using correlations?
I’m aware of the mean-variance framework where we construct a portfolio such that we attempt to minimise the variance and maximise returns.
What if instead we’re in a scenario where the main goal is ...
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Distribution of sample covariance times inverse covariance times sample covariance
I want to understand the distribution of the random variable:
$$S_n = \frac{1}{n^2} 1'\hat \Sigma \Sigma ^{-1} \hat \Sigma 1$$.
1 is a vector of ones of size n, and the variance is of size nxn. $\hat \...
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Optimal weights in portfolio after rebalancing
I have a quite simple question but while looking for answers in research papers I couldn't find anything. The question can be summarized as : if you expect a shock on an asset, why don't you rebalance ...
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Question about marginal risk contribution / portfolio volatility decomposition
I am trying to understand the rule where you add a new asset to a portfolio if its Sharpe ratio is greater than the product of the portfolio sharpe ratio and the correlation between the portfolio and ...
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Application of Leverage in Different Interest Rate Environments to an Efficient Portfolio
I have read that some Institutional Investors are utilizing leverage. According to Modern Portfolio Theory, to apply leverage one would:
a) find the tangency portfolio on the efficient frontier from ...
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Calculating marginal risk contribution of FX for foreign asset portfolio
I am a European investor investing in US equities. My US equities portfolio returns in EUR can be broken down into (1) equities returns in USD terms, and (2) USDEUR spot currency returns.
Using the ...
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Analytical solution to short-sale constrained portfolio
Say that we want to find the efficient mean-variance portfolio (i.e. minimize variance given that weights sum to 1 and given a set target return) and impose a short sale constraint such that $w_i \geq ...
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What is Ei in paper "How to Combine a Billion Alphas" by Zura Kakushadze? [closed]
I am reading paper "How to Combine a Billion Alphas" by Zura Kakushadze.
In the paper, it has Ei which are the expected returns for alphas.
It also has Ri hat as follows. I wonder what the ...
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Why not inequality constraint in mean-variance portfolio optimization?
Question 1:
In Modern Portfolio Theory, the case where we minimize variance given a set return and that the weights sum to 1, why is the return set as an equality constraint, not an inequality?
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